This section illustrates one strategy for finding ‘original’ prices from discounted and marked-up prices. Using a double number line can help learners visualise how to get to the answer, and gives them a problem-solving tool for percentages that they can use in other contexts. This teaching approach helps learners build number sense.

Pre-Discount Price

Often we see sale prices advertised after a percentage discount has been taken off. How do we work out what the original price was?

The sale price is $960, how can we work out what the original price was?

The original price is always 100% or the whole.

The sale price is 85% of the original price (100% - 15%).

Use what you know about 85% to find 1%

$960 represents 85%; so if we divide 960 by 85 we find the value of 1% is $11.29.

Use 1% to find 100%

To find 100%, we multiply the value of 1% by 100. This gives the original price.

Summarise the problem

$960 ÷ 85 = 11.29 or 1%.

$11.29 x 100 = $1129 or 100%

$1129.00 is the original price.

Ask your learners how the working would change if the discount was 25% or 30%. Get them to try and generalise the steps for any percentage discount.

Pre-Marked Up (Wholesale) Price

A business shirt retails for $159.90 (excluding GST) after a 30% mark-up. What is the wholesale price (price before the mark-up)?

Again, we’re looking for the original (wholesale) price which is 100%, but in this example we are given a marked up price which represents 130% of the wholesale price.

Use what you know about 130% to find 1%

$159.90 represents 130%; so if we divide 159.90 by 130 we find the value of 1% is $1.23.

Use 1% to find 100%

1% is $1.23, so multiply by 100 get the wholesale price (100%).

Summarise the problem

159.90 ÷ 130 = $1.23 or 1%

$1.23 x 100 = $123.00 or 100% (Wholesale Price)

Ask your learners how the working would change if the mark-up was 25% or 40%. What about a mark-up of 125%? Get them to try and generalise the steps for any percentage mark-up.